Calculate all properties of a regular hexagon including area, perimeter, side length, apothem, radius, and diagonals. Enter any known value for instant results.
A regular hexagon is a six-sided polygon where all sides are equal length and all interior angles are 120°. It's one of the most efficient shapes in nature, famously used by bees in honeycombs to maximize storage while minimizing material.
For a regular hexagon with side length s, the area formula is A = (3√3/2)s², which simplifies to approximately 2.598s². For example, if the side is 5 units, the area is (3√3/2) × 5² = 2.598 × 25 ≈ 64.95 square units.
The apothem is the distance from the center of the hexagon to the midpoint of any side. For a regular hexagon, apothem = (√3/2)s, where s is the side length. It's also the height of each of the 6 equilateral triangles that make up the hexagon.
The radius (circumradius) goes from the center to a vertex (corner), while the apothem goes from the center to the midpoint of a side. In a regular hexagon, radius = side length, and apothem = (√3/2) × side length. The apothem is always shorter than the radius.
A hexagon has 9 diagonals total: 3 long diagonals (connecting opposite vertices) and 6 short diagonals (connecting vertices separated by one vertex). The long diagonals are twice the side length (2s), and short diagonals are √3 times the side length (√3·s).
Hexagons are the most efficient shape for dividing a surface into equal areas with minimal perimeter. This is why bees use hexagonal cells in honeycombs - it uses the least wax while providing maximum storage space. This property makes hexagons ideal for tessellation (tiling without gaps).
Yes! Regular hexagons are one of only three regular polygons that can tile a flat surface with no gaps (the others are triangles and squares). This is because the interior angle of 120° allows exactly three hexagons to meet at each vertex (3 × 120° = 360°).
The perimeter of a regular hexagon is simply P = 6s, where s is the side length. Since all six sides are equal, you just multiply the side length by 6. For example, a hexagon with 5-unit sides has a perimeter of 30 units.
A regular hexagon can be divided into 6 equilateral triangles, all meeting at the center. Each triangle has a side length equal to the hexagon's side. This is why the radius equals the side length - the radius forms one side of these equilateral triangles.
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